Download IOSR Journal of Computer Engineering (IOSR-JCE)

IOSR Journal of Computer Engineering (IOSR-JCE)
e-ISSN: 2278-0661, p- ISSN: 2278-8727Volume 9, Issue 5 (Mar. - Apr. 2013), PP 75-81
www.iosrjournals.org
Survey: Efficent tree based structure for mining frequent pattern
from transactional databases
Hitul Patel1, Vinit Kumar2, Puspak Raval3
1
2
Department of Computer Engineering, Hasmukh Goswami College of Engineering, Vehlal, Gujarat
Department of Computer Engineering, Hasmukh Goswami College of Engineering, Vehlal, Gujarat
3
Department of Computer Engineering, DAIICT, Gandhinagar, Gujarat
Abstract: Different types of data structure and algorithm have been proposed to extract frequent pattern from
a given databases. Several tree based structure have been devised to represent the data for efficient frequent
pattern discovery. One of the fastest and efficient frequent pattern mining algorithm is CATS algorithm which
represent the data and allow mining with a single scan of database. CATS tree can be used with incremental
update of the database. Transaction can be added or removed without rebuilding of the whole data structure.
Keywords – Frequent Pattern Mining, Transactional Databases, Minimum Support, Itemsets.
I.
Introduction
One of the major function of association rules is to analyse large amount of databases. Association
rules have been applied to many areas including classification, clustering, detection. The mining process can be
broken down into frequent itemsets and the generation of association rules. Association rules is an iterative
process. Frequent Pattern Mining plays a very dominant role in data mining. There are many various application
such as text, transaction database and image processing to generate a large volume of data[3,9].
For frequent pattern mining the algorithm are divided into two categories 1) Apriori algorithm, 2) Tree
structure algorithm. The apriori algorithm is an influential algorithm for mining frequent item sets for
association rules. The apriori based algorithm uses a generate and test strategy approach to find frequent pattern
by constructing candidate items and checking their counts and frequency from transactional databases. The tree
structure algorithm uses a text only approach. There is no need to generate candidate items sets[7]. Several tree
based structure have been devised to represent the data for efficient pattern discovery. Most of the tree based
structure allow efficient mining with single scan over the database. One of the fastest and efficient frequent
pattern mining algorithm is CATS algorithm[10]. The CATS algorithm enable frequent pattern mining with
different support value without rebuild the whole structure. In addition CATS tree allow removal of transaction
concurrently. Although a large database can be processed by CATS tree if out – of – date transaction are
removed concurrently. CATS-FELINE uses a divide and conquer method to generate frequent pattern without
generating candidate item sets. In order to ensure that all frequent pattern are captured by FELINE, FELINE has
to traverse both up n down to include all frequent items. While building conditional condensed CATS tree, items
are executed if the items are mined or if the items are infrequent.
II.
Literature Survey
2.1 FP - Tree( Frequent Pattern Tree)
Frequent Pattern Tree is one of the oldest tree structure approaches that don’t use candidate set
generation adopted by apriori based algorithm. From a given set of transactional data it first construct a tree
structure in which all items are arranged in descending order according to their frequency.After construction of
FP tree the frequent pattern can be mined using an iterative algorithm which looks up the header table and select
the item with minimum support[6]. Then the infrequent items are removed from existing node and remaining
items are reordered as the frequent item-sets at the specified items.The items that does not meet the minimum
threshold has been eliminated.
Consider the transactional database shown in Table 1 with 5 transactions.
Tran. ID Items
T1
A,B,D,E
T2
A,C,D
T3
E,F,H,I
T4
A,B
T5
C,E,F
Table 1. Example of Transactional Database [7]
www.iosrjournals.org
75 | Page
Survey: Efficent tree based structure for mining frequent pattern from transactional databases
The frequent itemlist for the above database is given in Table 2.
Items
Count
A
3
B
2
C
2
D
2
E
3
F
2
H
1
I
1
Table 2. Frequent Itemlist for the Transactional Database in Table1[7]
The items that does not meet the minimum threshold has been eliminated. The frequent itemlist that support the
minimum support threshold is given in Table 3.
Items Count
A
3
E
3
B
2
C
2
D
2
F
2
Table 3. Frequent Itemlist for the Transactional Database that Support Minimum Threshold [7]
The transactional database according to the frequent item list is given in Table 4.
Tran. ID Items
T1
A,E,B,D
T2
A,C,D
T3
E,F
T4
A,B
T5
E,C,F
Table 4. Sorted and Eliminated Transactions of the Database in Table 1 [7]
Figure 1. Steps in creating the FP – Tree [7]
www.iosrjournals.org
76 | Page
Survey: Efficent tree based structure for mining frequent pattern from transactional databases
Consider the itemset D. Its prefix paths are {((A,E,B):1),((A,C):1)}. After removing the infrequent
items,(A:2).So the frequent itemset for D is A.
2.1.1 Advantages
The main advantage of FP tree is that it does not generate any candidate items. It has only 2 passes over
the data sets. FP tree is much faster then Apriori algorithm. FP tree uses a compact data structure. Another
advantage is that it eliminate repeated database scan.
2.1.2 Disadvantages
The main disadvantage is that FP tree may not fit into memory. Another Disadvantage is that FP tree is
expansive to build. FP tree suffer from temporal locality issues.
2.2 CAN Tree (Canonical Tree)
A CAN tree that arrange the nodes of a tree in some canonical tree. CAN tree generate a tree structure
similar to the FP tree algorithm. Compare to FP tree it does not require a rescan of the original database once it
is updated[3]. CAN tree contains all the transaction in canonical order hence the order of the node in CAN tree
will not unaffected by any incremental updates like insertion, deletion and modification of the transactions.
Consider the following database,
DB
Original database
DB1
1
DB2
st
TID
T1
T2
T3
Items
{a,c,d,g}
{b,c,d,e}
{b}
group of insertions
T5
{a,e,f}
group of insertions T6
{b,c}
T7
{a}
Table 5. Example of Transactional Database [7]
2
nd
www.iosrjournals.org
77 | Page
Survey: Efficent tree based structure for mining frequent pattern from transactional databases
2.2.1 Advantages
The main advantage is it support incremental support without any changes in the tree structure. There is no
need to rescan the database when it is updated.
2.3 COFI Tree
COFI tree is much faster than the FP Growth tree and it require significantly less memory. The basic
idea of COFI tree is to build a projections from the FP tree each corresponding to sub-transactions of items with
a given frequent item. The COFI tree algorithm uses a top down approach where it’s performance shows to be
severely affected while mining databases that has potentially long candidate pattern that turns to be not
frequent[7].
The basic idea behind COFI tree is simple and is based on maximal frequent patterns. A frequent item
set X is said to be maximal if there is no frequent item set X’ such that X X’. Maximal frequent pattern are a
relatively small subset of all frequency item sets.
Let us assume that In Oracle we knows all the maximal frequent item sets in a transactional database so
deriving all frequent item sets becomes trivial. The Oracle does not exist but propose a pseudo-oracle that
discover this maximal frequent pattern using the COFI tree and we derive all item sets from them.
Consider the following database,
D
E
A
B
D
F
E
H
A
G
D
E
C
B
A
G
D
F
E
I
A
G
E
B
F
C
A
D
H
E
F
A
G
D
B
L
A
B
C
F
A
D
B
C
G
A
F
B
C
E
A
B
C
H
C
Table 6.Example of Transactional database [7]
A
10
B
8
C
7
D
7
E
7
F
G
H
6
5
3
Figure 6. Creation of COFI Tree [7]
2.3.1 Advantages
This method is advantageous because the size of the generated candidate item list is minimized. This
algorithm built and efficient mined one at a time making memory significantly small.
www.iosrjournals.org
78 | Page
Survey: Efficent tree based structure for mining frequent pattern from transactional databases
2.3.1 Disadvantages
It is disadvantageous because maximum effort is required for minimization.
2.4 CATS Tree
CATS tree is an extension of FP tree. CATS tree[7] is a prefix tree and it contains all element of the FP
tree including the header and the item links. To improve storage compression and allow frequent pattern mining
without generating candidate itemsets we use CATS-tree algorithm. CATS tree algorithm enable frequent
pattern mining with different support without re-building the tree structure. This algorithm allow single pass
over the database. It also allow efficient insertion and deletion of transaction at any time. In other word
transaction can be added to or removed from the tree at any time. CATS tree contains all items in every
transaction. In CATS tree ordrer of the items within paths from the roots to leaves are ordered by local
support.The main properties of CATS tree is it’s Compactness. Compactness measures how many transactions
are sharing a node. It is possible to create a CATS tree with maximum compression.
TID items
T1 {a,c,d,g}
DB Original database T2 {b,c,d,e}
T3 {b}
1st group of
DB1 insertions
T5 {b,e,f}
2nd group of
DB2 insertions
T6 {b,c}
T7 {b}
Table 7. Example of Transactional Database [7]
The steps in the construction of CATS tree is illustrated in Figure 7.
a:1
c:2
c:1
d:2
d:1
a:1
b:1
g:1
g:1
e:1
(a)
(b)
b:2
c:2
d:2
a:1
e:1
g:1
(c)
Figure 7. Steps in Creation of CATS tree [7]
www.iosrjournals.org
79 | Page
Survey: Efficent tree based structure for mining frequent pattern from transactional databases
b:3
c:2
e:1
d:2
f:1
a:1
e:1
g:1
Figure 8. CATS tree after 1st group of insertions [7]
b:4
a:1
g:1
b:5
c:3
e:1
c:3
e:1
d:2
f:1
d:2
f:1
e:1
a:1
e:1
g:1
(a)
(b)
Figure 9. CATS tree after 2
nd
group of insertions[7]
After constructing the CATS tree, the frequent patterns can be found by following the frequency of an item by
considering its both upward and downward paths.
2.4.1 Advantages
The main advantage is that the database is scan only once and the tree are reordered according to their
local frequency in the paths. The disadvantage is that a lot of computation are required to build the tree
structure. CATS tree algorithm allow addition and deletion of transaction in a single transaction. CATS tree
algorithm is suitable for frequent pattern mining where modification and frequent pattern are common.
2.4.2 Disadvantages
The main disadvantage is that it require more computation to build a tree.
2.5 CATS – FELINE
CATS – FELINE algorithm employs divide and conquer method to generate frequent pattern without generating
candidate itemsets. This algorithm partititon the data based on what pattern transacrions have.
CATS – FELINE algorithm builds a conditional condensed CATS-tree for each frequent item p by gathering all
transactions that contain p. In conditional condensed CATS- tree all infrequent items are removed and is
different from FP tree. All Frequent pattern are captured by CATS-FELINE, it has to traverse both up and down
the CATS tree.
2.5.1 Algorithm for a Conditional Condensed Tree
Like CATS-FELINE the mining process proceeds in three steps:
Step 1: First convert the CATS tree generated from scanning a database into condensed tree. All the nodes
having the minimum support are removed from the tree.
www.iosrjournals.org
80 | Page
Survey: Efficent tree based structure for mining frequent pattern from transactional databases
Step 2: Now construct condtional condensed CATS-tree for items in the header table having greater than the
minimum support.
Step 3: For conditional condensed CATS-tree generated from step 2, items with atleast minimum support are
frequently mined.
III.
Conclusion and Prospect
In this paper it is summarised that various data structure that can be used to extract frequent pattern
from a large database. We have discussed about the structure like CAN tree, FP tree, CATS tree with their
advantages and disadvantages. Among the discussion on the above structure CATS tree can be considered to
optimal because it scans the database only once and transaction can be added or removed from the tree at any
time. As well as CATS tree may be suitable for any incremental update in the database. This makes CATS tree
algorithm suitable for real time transactional frequent pattern mining where frequent pattern are common.
It can be conclude that some research direction for mining frequent pattern from a transactional
databases by existing work in future. As the future scope, the number of database scan, execution time, memory
usage may still be decrease by investigating other kind of algorithm.
Acknowledgment
I would be thankful to my guide assistant professor Vinitkumar Gupta here for fervent help when I have some troubles in paper
writing. I will also thank my class mates in laboratory for their concern and support both in study and life.
References
Muthaimenul Adnan and Reda Alhajj, “A Bounded and Adaptive Memory-Based Approach to Mine Frequent Patterns From Very
Large Databases” IEEE Transactions on Systems Management and Cybernetics- Vol.41,No. 1,February 2011.
[2] W. Cheung and O. R. Zaiane, “Incremental mining of frequent patterns without candidate generation or support constraint,” in Proc.
IEEE Int.Conf. Database Eng. Appl., Los Alamitos, CA, 2003, pp. 111–116.
[3] C. K.-S. Leung, Q. I. Khan, and T. Hoque, “Cantree: A tree structure for efficient incremental mining of frequent patterns,” in Proc.
IEEE Int.Conf. Data Minig, Los Alamitos, CA, 2005,pp. 274-281
[4] M.El-Hajj and O.R. Zaiane, “COFI approach for mining frequent itemsets revisited,” In Proc. ACM SIGMOD Worksjop Res. Issues
Data Mining knowl. Discovery, New York, 2004, pp. 70-75
[5] B. Rácz, “nonordfp: An FP-growth variation without rebuilding the FP-tree,” in Proc. FIMI, 2004
[6] J. Pei, J. Han, and L.V.S. Lakshmanan.“Mining frequent itemsets with convertible constraints”, In Proc. ICDE 2001, pp. 433–442
[7] K. Sasireka, G.Kiruthinga, K.Raja, “A survey about Various Data Structures For Mining Frequent Patterns from Large Database,”
International Journal of Research and Reviews in Information Sciences(IJRRIS) Vol. 1, No. 3, September 2011, ISSN: 2046-6439.
[8] C.K.-S. Leung. Interactive constrained frequent-pattern mining system.In Proc.IDEAS 2004, pp. 49–58.
[9] R. Agrawal and R. Srikant, “Fast algorithms for mining association rules”, Proc. of the 20th Very Large Data Bases International
Conference, (1994), pp. 487-499, Santiago, Chile.
[10] W. Cheung, and O. Zaiane, “Incremental Mining of Frequent Patterns Without Candidate Generation or Support Constraint”, Proc. of
7th International Database Engineering and Applications Symposium, (2003), pp. 111–116, Los Alamitos, CA.
[11] Agrawal, Rakesh; Srikant, Ramakrishnan: “Fast Algorithms for Mining Association Rules.” Proc. 20th Int Conf. Very Large Data
Bases, VLDB, 1994.
[1]
www.iosrjournals.org
81 | Page